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The method of fundamental solutions for the solution of steady-state free boundary problems. (English) Zbl 0745.65075
The author discusses the method of fundamental solutions and its application to free boundary problems. He gives the results obtained by using the method for a problem with a known exact solution and compares the results, and notes that a drawback is that boundary singularities tend to move to the interior of the domain under consideration. Solutions, in the form of graphs are given for three problems: seepage through a rectangular porous dam, Riabouchinsky cavity flow and flow over a weir. He points out that where there are boundary singularities, it may be necessary to use a very large number of degrees of freedom.

MSC:
65Z05 Applications to the sciences
35R35 Free boundary problems for PDEs
76S05 Flows in porous media; filtration; seepage
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
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